Hole-doped Regime Research Articles

Phonon-mediated unconventional superconductivity in rhombohedral stacked multilayer graphene

Understanding the origin of superconductivity in correlated two-dimensional materials is a key step in leveraging material engineering techniques for next-generation nanoscale devices. While it is widely accepted that phonons fluctuations only mediate conventional (s-wave) superconductivity, the common phenomenology of superconductivity in Bernal bilayer and rhombohedral trilayer graphene, as well as in a large family of graphene-based moiré systems, suggests a common superconducting mechanism across these platforms. In particular, in all these platforms some superconducting regions violate the Pauli limit, indicating unconventional superconductivity, naively ruling out conventional phonon-mediated pairing as the underlying mechanism. Here we combine first principles simulations with effective low-energy theories to investigate the superconducting mechanism and pairing symmetry in rhombohedral stacked graphene multilayers. We find that phonon-mediated superconductivity explains the main experimental findings, namely the displacement field and doping level dependence of the critical temperature, and the presence of two superconducting regions with different pairing symmetries that depend on the parent normal state. In particular, we find that intra-valley phonon scattering favors a triplet f-wave pairing when combined with electronic correlations stabilizing a spin- and valley-polarized normal state. We also propose a so far unexplored superconducting region at higher hole doping densities nh ≈ 4 × 1012 cm−2, and demonstrate how this highly hole-doped regime can be reached in heterostructures consisting of monolayer α-RuCl3 and rhombohedral trilayer graphene. Our findings promote phonon-mediated pairing as a strong contender to explain superconductivity across a wide range of graphene platforms, and demonstrate that phonons can, in fact, stabilize unconventional superconducting orders.

Local Gate Enhanced Correlated Phases in Twisted Monolayer-Bilayer Graphene.

Manipulating the flat band degeneracy and thus getting the correlated insulating phases has been an ideal thread for realizing the exotic quantum phenomenon in the moiré system. To achieve this goal, the delicately tuned twist angle and a substantial displacement field (D) are rigorously requested. Here, we report our scanning tunneling microscope (STM) work on reaching these correlated insulating states in twisted monolayer-bilayer graphene through a decorated tip. It acts as a local top gate, leading to an enhanced local D, and enables us to fully lift the 8-fold degeneracy of the flat bands. With the aid of this technique, we further expand the correlated insulating states into a more tolerant twist angle that is down to 0.92°. Moreover, the correlated insulating phases in the hole-doping regime are realized. Our tip decoration method allows us to integrate the STM study with the high displacement field for the correlated phases in the twisted moiré systems.

Electronic Decoupling and Hole-Doping of Graphene Nanoribbons on Metal Substrates by Chloride Intercalation.

Atomically precise graphene nanoribbons (GNRs) have a wide range of electronic properties that depend sensitively on their chemical structure. Several types of GNRs have been synthesized on metal surfaces through selective surface-catalyzed reactions. The resulting GNRs are adsorbed on the metal surface, which may lead to hybridization between the GNR orbitals and those of the substrate. This makes investigation of the intrinsic electronic properties of GNRs more difficult and also rules out capacitive gating. Here, we demonstrate the formation of a dielectric gold chloride adlayer that can intercalate underneath GNRs on the Au(111) surface. The intercalated gold chloride adlayer electronically decouples the GNRs from the metal and leads to a substantial hole-doping of the GNRs. Our results introduce an easily accessible tool in the in situ characterization of GNRs grown on Au(111) that allows for exploration of their electronic properties in a heavily hole-doped regime.

Coexistence of superconductivity with partially filled stripes in the Hubbard model

The Hubbard model is an iconic model in quantum many-body physics and has been intensely studied, especially since the discovery of high-temperature cuprate superconductors. Combining the complementary capabilities of two computational methods, we found superconductivity in both the electron- and hole-doped regimes of the two-dimensional Hubbard model with next-nearest-neighbor hopping. In the electron-doped regime, superconductivity was weaker and was accompanied by antiferromagnetic Néel correlations at low doping. The strong superconductivity on the hole-doped side coexisted with stripe order, which persisted into the overdoped region with weaker hole-density modulation. These stripe orders varied in fillings between 0.6 and 0.8. Our results suggest the applicability of the Hubbard model with next-nearest hopping for describing cuprate high–transition temperature ( T c ) superconductivity.

Magnetism and Superconductivity in the t–J Model of La3Ni2O7 Under Multiband Gutzwiller Approximation

The recent discovery of possible high temperature superconductivity in single crystals of La3Ni2O7 under pressure renews the interest in research on nickelates. The density functional theory calculations reveal that both d z 2 and d x 2–y 2 orbitals are active, which suggests a minimal two-orbital model to capture the low-energy physics of this system. In this work, we study a bilayer two-orbital t–J model within multiband Gutzwiller approximation, and discuss the magnetism as well as the superconductivity over a wide range of the hole doping. Owing to the inter-orbital super-exchange process between d z 2 and d x 2–y 2 orbitals, the induced ferromagnetic coupling within layers competes with the conventional antiferromagnetic coupling, and leads to complicated hole doping dependence for the magnetic properties in the system. With increasing hole doping, the system transfers to A-type antiferromagnetic state from the starting G-type antiferromagnetic (G-AFM) state. We also find the inter-layer superconducting pairing of d x 2–y 2 orbitals dominates due to the large hopping parameter of d z 2 along the vertical inter-layer bonds and significant Hund’s coupling between d z 2 and d x 2–y 2 orbitals. Meanwhile, the G-AFM state and superconductivity state can coexist in the low hole doping regime. To take account of the pressure, we also analyze the impacts of inter-layer hopping amplitude on the system properties.

Discovery of charge order in a cuprate Mott insulator

Copper oxide superconductors universally exhibit multiple forms of electronically ordered phases that break the native translational symmetry of the CuO2 planes. In underdoped cuprates with correlated metallic ground states, charge/spin stripes and incommensurate charge density waves (CDWs) have been experimentally observed over the years, while early theoretical studies also predicted the emergence of a Coulomb-frustrated 'charge crystal' phase in the very lightly doped, insulating limit of CuO2 planes. Here, we search for signatures of CDW order in very lightly hole-doped cuprates from the 123 family RBa2Cu3O7 - δ (RBCO; R: Y or rare earth), by using resonant X-ray scattering, electron transport, and muon spin rotation measurements to resolve the electronic and magnetic ground states fully. Specifically, Pr is used to substitute Y at the R-site to systematically suppress the superconductivity and access the extremely low hole-doping regime of the cuprate phase diagram without changing the oxygen stoichiometry. X-ray scattering data taken on Pr-doped YBCO thin films reveal an in-plane CDW order that follows the same linear evolution of wave vector versus hole concentration as oxygen-underdoped YBCO but extends all the way to the insulating and magnetically ordered Mott limit. Combined with the recent observation of charge crystal phase on an insulating surface of Bi2Sr2CaCu2O8 + z, our results in RBCO suggest that this electronic symmetry breaking is universally present in very lightly doped CuO2 planes. These findings bridge the gap between the Mott insulating state and the underdoped metallic state and underscore the prominent role that Coulomb-frustrated electronic phase separation plays among all cuprates.

Competing chiral d -wave superconductivity and magnetic phases in the strong-coupling Hubbard model on the honeycomb lattice

We address the competing superconducting and magnetic phases on the honeycomb lattice, in a field-theoretic approach suitable to yield a low-energy perturbative theory for the strong-coupling limit of the Hubbard model, both at half filling and in the low and high hole-doped regimes. The effective low-lying Hamiltonian is presented in terms of charge (Grassmann fields) and spin [SU(2) gauge fields] degrees of freedom. We analyze the competing phases by calculating the ground-state energy, electronic spectrum, and other observables associated with the $s$- and ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}$-wave superconducting phases, doped antiferromagnetic, and doped ferromagnetic states. We find that, while the antiferromagnetic order has the lowest ground-state energy for low hole doping near half filling, a dominant superconducting state with chiral ${d}_{{x}^{2}\ensuremath{-}{y}^{2}}+i{d}_{xy}$-wave symmetry emerges in the vicinity of the Van Hove singularity in the high hole-doped regime, with the presence of a quantum first-order transition accompanied by spatial phase separation. We highlight that advances in the understanding of chiral superconducting states on the honeycomb lattice are relevant to a number of doped compounds including the graphene monolayer system.

Formation of CuO$_2$ sublattices by suppression of interlattice correlations in tetragonal CuO

We investigate the tetragonal phase of the binary transition metal oxide CuO (t-CuO) within the context of cellular dynamical mean-field theory. Due to its strong antiferromagnetic correlations and simple structure, analysing the physics of t-CuO is of high interest as it may pave the way towards a more complete understanding of high-temperature superconductivity in hole-doped antiferromagnets. In this work we give a formal justification for the weak-coupling assumption that has previously been made for the interconnected sublattices within a single layer of t-CuO by studying the non-local self-energies of the system. We compute momentum-resolved spectral functions using a Matrix Product State (MPS)-based impurity solver directly on the real axis, which does not require any numerically ill-conditioned analytic continuation. The agreement with photoemission spectroscopy indicates that a single-band Hubbard model is sufficient to capture the material’s low energy physics. We perform calculations on a range of different temperatures, finding two magnetic regimes, for which we identify the driving mechanism behind their respective insulating state. Finally, we show that in the hole-doped regime the sublattice structure of t-CuO has interesting consequences on the symmetry of the superconducting state.

Acoustic-phonon-mediated superconductivity in Bernal bilayer graphene

We present a systematic theory of acoustic-phonon-mediated superconductivity, which incorporates Coulomb repulsion, explaining the recent experiment in Bernal bilayer graphene under a large displacement field. The acoustic-phonon mechanism predicts that $s$-wave spin-singlet and $f$-wave spin-triplet pairings are degenerate and dominant. Assuming a spin-polarized valley-unpolarized normal state, we obtain $f$-wave spin-triplet superconductivity with a $T_c\sim 20$ mK near $n_e=-0.6\times 10^{12}$ cm$^{-2}$ for hole doping, in approximate agreement with the experiment. We further predict the existence of superconductivity for larger doping in both electron-doped and hole-doped regimes. Our results indicate that the observed spin-triplet superconductivity in Bernal bilayer graphene arises from acoustic phonons.

Quantum adiabatic doping for atomic Fermi-Hubbard quantum simulations

There have been considerable research efforts devoted to quantum simulations of Fermi-Hubbard model with ultracold atoms loaded in optical lattices. In such experiments, the antiferromagnetically ordered quantum state has been achieved at half filling in recent years. The atomic lattice away from half filling is expected to host d-wave superconductivity, but its low temperature phases have not been reached. In a recent work, we proposed an approach of incommensurate quantum adiabatic doping, using quantum adiabatic evolution of an incommensurate lattice for preparation of the highly correlated many-body ground state of the doped Fermi-Hubbard model starting from a unit-filling band insulator. Its feasibility has been demonstrated with numerical simulations of the adiabatic preparation for certain incommensurate particle-doping fractions, where the major problem to circumvent is the atomic localization in the incommensurate lattice. Here we carry out a systematic study of the quantum adiabatic doping for a wide range of doping fractions from particle-doping to hole-doping, including both commensurate and incommensurate cases. We find that there is still a localization-like slowing-down problem at commensurate fillings, and that it becomes less harmful in the hole-doped regime. With interactions, the adiabatic preparation is found to be more efficient for that interaction effect destabilizes localization. For both free and interacting cases, we find the adiabatic doping has better performance in the hole-doped regime than the particle-doped regime. We also study adiabatic doping starting from the half-filling Mott insulator, which is found to be more efficient for certain filling fractions.

Thermoelectric properties of tetragonal HfH2 under doping effect: First principles study

The effect of doping on the transport properties of HfH2 is explored using first-principles method and semi-classical Boltzmann approach. Thermoelectric properties such as electrical conductivity, Seebeck coefficient, electron and lattice thermal conductivity of doped and pure samples are calculated under various temperatures. The calculated results show that electrical and thermal conductivities increased with electron carrier concentrations similar to results reported by other studies in the low doping regime. While in the hole carrier concentration regime, irregular behavior is observed, especially in density of carriers equal to n = 4.6 × 1023 cm−3. Also, the lattice thermal conductivity and absolute value of Seebeck coefficient have been decreased with electron carrier concentration but these properties have irregular trend in the hole doping regime. Our results suggest that for achieving lower electron thermal conductivity with respect to pure HfH2, hole doping is much effective. Furthermore, the dispersive and large contribution of 5d orbital of Hf near the Fermi state and very low variation of L (Wiedemann-Franz factor) compared to the value of the free electron model L0, for pure and doped samples indicate that electrons in HfH2 have itinerant behavior and free-electron model is suitable to describe the transport properties of pure and doped samples of HfH2.

Autoionization and Dressing of Excited Excitons by Free Carriers in Monolayer WSe_{2}.

We experimentally demonstrate dressing of the excited exciton states by a continuously tunable Fermi sea of free charge carriers in a monolayer semiconductor. It represents an unusual scenario of two-particle excitations of charged excitons previously inaccessible in conventional material systems. We identify excited state trions, accurately determine their binding energies in the zero-density limit for both electron- and hole-doped regimes, and observe emerging many-body phenomena at elevated doping. Combining experiment and theory we gain access to the intra-exciton coupling facilitated by the interaction with free charge carriers. We provide evidence for a process of autoionization for quasiparticles, a unique scattering pathway available for excited states in atomic systems. Finally, we demonstrate a complete transfer of the optical transition strength from the excited excitons to dressed Fermi-polaron states as well as the associated light emission from their nonequilibrium populations.

Soft-Mode-Phonon-Mediated Unconventional Superconductivity in Monolayer 1T^{'}-WTe_{2}.

Recent experiments have tuned the monolayer 1T^{'}-WTe_{2} to be superconducting by electrostatic gating. Here, we theoretically study the phonon-mediated superconductivity in monolayer 1T^{'}-WTe_{2} via charge doping. We reveal that the emergence of soft-mode phonons with specific momentum is crucial to give rise to the superconductivity in the electron-doping regime, whereas no such soft-mode phonons and no superconductivity emerge in the hole-doping regime. We also find a superconducting dome, which can be attributed to the change of Fermi surface nesting conditions with electron doping. By taking into account the experimentally established strong anisotropy of temperature-dependent upper critical field H_{c2} between the in-plane and out-of-plane directions, we show that the superconducting state probably has the unconventional equal-spin-triplet pairing in the A_{u} channel of the C_{2h} point group. Our studies provide a promising understanding to the doping dependent superconductivity and strong anisotropy of H_{c2} in monolayer 1T^{'}-WTe_{2}, and can be extended to understand the superconductivity in other gated transition metal dichalcogenides.

Direct Visualization of Ambipolar Mott Transition in Cuprate CuO2 Planes

Identifying the essence of doped Mott insulators is one of the major outstanding problems in condensed matter physics and the key to understanding the high-temperature superconductivity in cuprates. We report real space visualization of Mott insulator-metal transition in Sr_{1-x}La_{x}CuO_{2+y} cuprate films that cover both the electron- and hole-doped regimes. Tunneling conductance measurements directly on the copper-oxide (CuO_{2}) planes reveal a systematic shift in the Fermi level, while the fundamental Mott-Hubbard band structure remains unchanged. This is further demonstrated by exploring the atomic-scale electronic response of CuO_{2} to substitutional dopants and intrinsic defects in a sister compound Sr_{0.92}Nd_{0.08}CuO_{2}. The results may be better explained in the framework of self-modulation doping, similar to that in semiconductor heterostructures, and form a basis for developing any microscopic theories for cuprate superconductivity.

Doping evolution of the magnetic excitations in the monolayer CuO2

In this paper, we study theoretically the doping evolution behaviors of the magnetic excitations (MEs) in the monolayer CuO2 grown on Bi2Sr2CaCu2O8+δ substrate. For the undoped system, the MEs exhibit the low energy commensurate behavior around (π, π). They turn to be incommensurate when the system is slightly hole-doped. In the intermediate doping regime, the low energy MEs diminish gradually. They turn to be dominated by the high energy modes. With further doping, an exotic structure transition of the MEs occurs in the heavily hole-doped regime which is directly related to the Lifshitz transition. Distinct MEs are separated by the transition point around which the low energy MEs exhibit the ring-like structure around (0, 0). Before the transition, the MEs are dominated by the broad particle–hole continuum at very high energies. In contrast, across the transition point, two new low energy modes develop around (0, 0) and (π, π) attributing to the intrapocket and interpocket particle–hole scatterings, respectively.

Nickelate superconductors: Multiorbital nature and spin freezing

Superconductivity with a remarkably high $T_c$ has recently been found in Sr-doped NdNiO$_2$ thin films. While this system bears strong similarities to the cuprates, some differences, such as a weaker antiferromagnetic exchange coupling and possible high-spin moments on the doped Ni sites have been pointed out. Here, we investigate the effect of Hund coupling and crystal field splitting in a simple model system and argue that a multiorbital description of nickelate superconductors is warranted, especially in the strongly hole-doped regime. We then look at this system from the viewpoint of the spin-freezing theory of unconventional superconductivity, which provides a unified understanding of unconventional superconductivity in a broad range of compounds. Sr$_{0.2}$Nd$_{0.8}$NiO$_2$ falls into a parameter regime influenced by two spin-freezing crossovers, one related to the emergent multi-orbital nature in the strongly doped regime and the other related to the single-band character and square lattice geometry in the weakly doped regime.

Phase stiffness in an antiferromagnetic superconductor

We analyze the suppression of the phase stiffness in a superconductor by antiferromagnetic order. The analysis is based on a general expression for the phase stiffness in a mean-field state with coexisting spin-singlet superconductivity and spiral magnetism. Neel order is included as a special case. Close to half-filling, where the pairing gap is much smaller than the magnetic gap, a simple formula for the phase stiffness in terms of magnetic quasi-particle bands is derived. The phase stiffness is determined by charge carriers in small electron or hole pockets in this regime. The general analysis is complemented by a numerical calculation for the two-dimensional Hubbard model with nearest and next-to-nearest neighbor hopping amplitudes at a moderate interaction strength. The resulting phase stiffness exhibits a striking electron-hole asymmetry. In the ground state, it is larger than the pairing gap on the hole-doped side, and smaller for electron doping. Hence, in the hole-doped regime near half-filling the ground state pairing gap sets the scale for the Kosterlitz-Thouless temperature T_c^{KT}, while in the slightly electron-doped regime T_c^{KT} is determined essentially by the ground state phase stiffness.

Momentum-dependent relaxation dynamics of the doped repulsive Hubbard model

We study the dynamical behavior of doped electronic systems subject to a global ramp of the repulsive Hubbard interaction. We start with formulating a real-time generalization of the fluctuation-exchange approximation. Implementing this numerically, we investigate the weak-coupling regime of the Hubbard model both in the electron-doped and hole-doped regimes. The results show that both local and nonlocal (momentum-dependent) observables evolve toward a thermal state, although the temperature of the final state depends on the ramp duration and the chemical doping. We further reveal a momentum-dependent relaxation rate of the distribution function in doped systems, and trace back its physical origin to the anisotropic self-energies in the momentum space.

Lieb and hole-doped ferrimagnetism, spiral, resonating valence-bond states, and phase separation in large-U AB2 Hubbard chains

The ground state (GS) properties of the quasi-one-dimensional AB2 Hubbard model are investigated taking the effects of charge and spin quantum fluctuations on equal footing. In the strong-coupling regime, a functional integral representation allows us to derive a low-energy Lagrangian suitable to describe the ferrimagnetic phase at half filling and the phases in the hole-doped regime. At half filling, a perturbative spin-wave analysis allows us to find the GS energy, sublattice magnetizations, and total spin per unit cell in the Lieb ferrimagnetic GS of the effective quantum Heisenberg model, in very good agreement with previous results. In the challenging hole doping regime away from half filling, we derive the corresponding Hamiltonian. Under the assumption that charge and spin quantum correlations are decoupled, the evolution of the second-order spin-wave modes in the doped regime unveils the occurrence of spatially modulated spin structures and the emergence of phase separation in the presence of resonating-valence-bond states. We also calculate the doping-dependent GS energy and total spin per unit cell, including both Zeeman and orbital contributions, in which case it is shown that the spiral ferrimagnetic order collapses at a critical hole concentration. Notably, our analytical results in the doped regime are in very good agreement with density matrix renormalization group studies, where our assumption of spin-charge decoupling is numerically supported by the formation of charge-density waves in anti-phase with the modulation of the magnetic structure.

Spin transport in high-mobility graphene on WS2 substrate with electric-field tunable proximity spin-orbit interaction

Graphene supported on a transition metal dichalcogenide substrate offers a novel platform to study the spin transport in graphene in the presence of a substrate-induced spin-orbit coupling while preserving its intrinsic charge transport properties. We report the first nonlocal spin transport measurements in graphene completely supported on a 3.5-nm-thick tungsten disulfide (${\mathrm{WS}}_{\text{2}}$) substrate, and encapsulated from the top with an 8-nm-thick hexagonal boron nitride layer. For graphene, having mobility up to 16 000 ${\mathrm{cm}}^{2}\phantom{\rule{0.16em}{0ex}}{\mathrm{V}}^{\ensuremath{-}1}\phantom{\rule{0.16em}{0ex}}{\mathrm{s}}^{\ensuremath{-}1}$, we measure almost constant spin signals both in electron and hole-doped regimes, independent of the conducting state of the underlying ${\mathrm{WS}}_{2}$ substrate, which rules out the role of spin-absorption by ${\mathrm{WS}}_{2}$. The spin-relaxation time ${\ensuremath{\tau}}_{\text{s}}$ for the electrons in graphene-on-${\mathrm{WS}}_{2}$ is drastically reduced down to $\ensuremath{\sim}10$ ps from ${\ensuremath{\tau}}_{\text{s}}\ensuremath{\sim}800$ ps in graphene-on-${\mathrm{SiO}}_{2}$ on the same chip. The strong suppression of ${\ensuremath{\tau}}_{\text{s}}$ along with a detectable weak antilocalization signature in the quantum magnetoresistance measurements is a clear effect of the ${\mathrm{WS}}_{2}$-induced spin-orbit coupling (SOC) in graphene. Via the top-gate voltage application in the encapsulated region, we modulate the electric field by 1 V/nm, changing ${\ensuremath{\tau}}_{\text{s}}$ almost by a factor of four, which suggests electric-field control of the in-plane Rashba SOC. Further, via the carrier-density dependence of ${\ensuremath{\tau}}_{\text{s}}$, we also identify the fingerprints of the D'yakonov-Perel' type mechanism in the hole-doped regime at the graphene-${\mathrm{WS}}_{2}$ interface.